We report the discovery of shocked molecular and ionized gas resulting from jet-driven feedback in the compact radio galaxy 4C 31.04 using near-IR imaging spectroscopy. 4C 31.04 is a $sim 100$ pc double-lobed Compact Steep Spectrum source believed to be a very young AGN. It is hosted by a giant elliptical with a $sim 10^{9}~rm M_odot$ multi-phase gaseous circumnuclear disc. We used high spatial resolution, adaptive optics-assisted $H$- and $K$-band integral field Gemini/NIFS observations to probe (1) the warm ($sim 10^3~rm K$) molecular gas phase, traced by ro-vibrational transitions of $rm H_2$, and (2), the warm ionized medium, traced by the [Fe II]$_{1.644~rm mu m}$ line. The [Fe II] emission traces shocked gas ejected from the disc plane by a jet-blown bubble $300-400~rm pc$ in diameter, whilst the $rm H_2$ emission traces shock-excited molecular gas in the interior $sim 1~rm kpc$ of the circumnuclear disc. Hydrodynamical modelling shows that the apparent discrepancy between the extent of the shocked gas and the radio emission can occur when the brightest regions of the synchrotron-emitting plasma are temporarily halted by dense clumps, whilst less bright plasma can percolate through the porous ISM and form an energy-driven bubble that expands freely out of the disc plane. This bubble is filled with low surface-brightness plasma not visible in existing VLBI observations of 4C 31.04 due to insufficient sensitivity. Additional radial flows of jet plasma may percolate to $sim rm kpc$ radii in the circumnuclear disc, driving shocks and accelerating clouds of gas, giving rise to the $rm H_2$ emission.
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